Because of problems at SourceForge's network provider, access to Tunnelblick downloads has been unreliable for the past fourteen hours or so. [1]
The Tunnelblick website, IP address checking, and update checking site are all working OK.
Only the binary downloads are problematic because only they are hosted by SourceForge. (In other words, a check for an update will succeed and say whether or not an update is needed, but an attempt to download the update may fail.)
If you are having a problem, try using a VPN! The different IP address or routing may work. (It does for me.)
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"SourceForge's network provider is currently experiencing connectivity routes with poor or inoperable performance. This will be fixed ASAP."
It isn't just SourceForge, Slashdot has the same problem.
To give you an idea of how random the problem is: one of my two IPv4 addresses works reliably; the other cannot load at all. Both addresses are from the same ISP (Cablevision's Optimum Internet in Connecticut USA) but they are are completely different addresses (all four quads are different) and they use slightly different routes to get to SourceForge. (A traceroute shows that even the failing one gets to SourceForge, but no response is ever received.)